Question: $ -\dfrac{6}{4} \div \left(\dfrac{4}{2} \div \dfrac{3}{9}\right) = {?} $
Solution: First, we can simplify the problem: $ -\dfrac{3}{2} \div \left(2 \div \dfrac{1}{3}\right) = {?} $ Dividing by a fraction is the same as multiply by the reciprocal of that fraction. $ = -\dfrac{3}{2} \div \left(2 \times 3\right) $ $ = -\dfrac{3}{2} \div \left(\dfrac{2 \times 3} {1 \times 1}\right) $ $ = -\dfrac{3}{2} \div \dfrac{6}{1} $ $ = -\dfrac{3}{2} \times \dfrac{1}{6} $ $ = \dfrac{-3 \times 1}{2 \times 6} $ $ = -\dfrac{3}{12}$ Simplify: $ = -\dfrac{1}{4}$